263-266] The Process of Fission 253 



264. Sir G. Darwin further supposed that immediately after fission the 

 periods of rotation of the two masses and the period of revolution about one 

 another would all three coincide, so that the system would rotate as a rigid 

 body. There is no longer the same justification for this "supposition when it 

 is recognised that fission occurs only after cataclysmic motion. 



We may however notice that only one vibration is unstable at the point 

 of bifurcation at which cataclysmic motion begins; this vibration is one in 

 which neither half of the mass gains upon the other either in rotation or 

 revolution. When the elongation of the pear-shaped figure first takes place, 

 the pointed end of the pear must, on account of conservation of angular 

 momentum, lag somewhat behind the rotation of the blunter end, but any 

 such difference of rotation produces a distortion which corresponds to a stable 

 vibration : forces of restitution at once come into play and equalise the angular 

 velocities. Similar forces of restitution will be in operation right up to the 

 instant of fission, so that in the final system the rotations may be expected to 

 agree with the revolution, both in period and in phase. The stars will 

 accordingly rotate about one another like a rigid body except for the slight 

 eccentricity of orbit discovered in the preceding section. 



Comparison with Observation 



265. These theoretical conclusions are borne out by observation on stars 

 of the ft Lyrae type *. In stars of this type the light curve varies continuously, 

 shewing that the masses must be either in actual contact or close to actual 

 contact as in fig. 34 (p. 163). Any difference in the periods of rotation and 

 revolution would shew itself in nonperiodicity of the light curve; of this 

 there is no evidence whatever. The eccentricity of orbit is invariably small, 

 being about 0'02 for ft Lyrae, X Carinae and RR Centauri, in which the 

 separation calculated from the light curve is zero or negative (corresponding 

 to imperfect fission), and being 0'03 for U Pegasi in which the separation is 

 excessively small. 



The periods are short, varying from 14 h. 32 m. for RR Centauri to 12*908 

 days for ft Lyrae. 



MOTION SUBSEQUENT TO FISSION 



Tidal Friction 



266. Darwin has shewn the importance of tidal friction in the subsequent 

 motion. As the stars shrink, the rate of rotation of each will increase in 

 accordance with the conservation of angular momentum, so that the rotations 

 of the separate masses will gain on their revolution about one another, and 



* Campbell, Stellar Motions, Table XXXI. 



